I am personally of the opinion that if someone ended up hurt by your actions then it's worth giving a genuine apology as you have a scenario where someone was hurt by something you did.
Now, there are many caveats to this:
Apologizing to narcissists as Ozy pointed out is a bad idea.
Apologizing to bad faith actors or manipulators is similarly a bad idea
Apologizing to those that are chronically unapologetic themselves is a bad idea (although someone has to apologize first, and so it can often be worth it to just bite the bullet and be the first to apologize. If they apologize back then, great, feud ended and you can work towards reconciliation. If they don't, we'll now you know they're not worth your time)
Apologizing when you didn't actually do anything wrong - well apologizing is probably a worse word than something like reconciliation. But they look similar so it's worth mentioning here. You can still work to reconcile a misunderstanding even if you don't believe yourself to have any fault. Recognizing genuine remorse over someone being hurt and working on ways to prevent such misunderstandings in the future is often not only enough, but is likely to be much more genuine than the kinds of fake token apologies you get from people who don't view themselves as at fault.
That last one is something that I think many, many people struggle with, and being able to resolve misunderstandings is a skill that requires both a degree of emotional intelligence as well as the humility to swallow one's pride.
And this isn't all to say that one should just capitulate on their principles in the interest of not hurting others. Part of the process of working on ways to prevent misunderstandings could be a recognition that the two of you are mutually incompatible, perhaps due to opposing principles, beliefs, personalities, or ideas. In which case the path forwards would be to just avoid future interactions.